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U.S. corporate pension funds are in the best shape they've been in since before the 2008 financial crisis as their shortfalls were cut nearly in half in 2013. Credit surely goes to the rising stock market, but last year's improvement in the funds' positions also owed much to the rise in bond yields.

Indeed, fully closing the gap between pension funds' assets and their future liabilities may depend more on higher interest rates than continued gains in the stock market.

Corporate pension plans among the Standard & Poor's 500 companies were last fully funded in 2007, before the financial near-meltdown of the following year. From 2009 to 2012, the plans' underfunding ranged between 16% and 23% -- with the worst shortfall in 2012, when S&P 500 index already had made a huge recovery from its recession lows.

These data cover the traditional, defined-benefit plans that were the norm for Corporate America a generation ago. As S&P Credit Week observes, U.S. companies have dealt with the burden of pension costs by shifting it to employees with defined-contribution plans such as 401(k) plans. The result: 46% of workers had saved $10,000 or less for retirement while an additional 20% had socked away between $10,000 and $49,900, according to a 2013 study by the Employee Benefit Research Institute. Only half of all workers receive any retirement benefits from their employers.

For those lucky enough to look forward to a monthly check in retirement, their employers have to set aside and invest funds to meet those obligations. Among the S&P 500 companies, 51 were fully funded at the end of 2013, up from just 18 in 2012.

There was another, less obvious boost to corporate pension plans in 2013: higher bond yields. Given that the jump in yields, which took the benchmark 10-year Treasury to 3% from a low of about 1.65%, resulted in bond price declines and negative returns from investment-grade debt last year, that might seem counterintuitive.

But the higher yields lowered the present value of future pension fund liabilities. (A higher discount rate for a stream of future payments lowers that stream's discounted present value. At a higher interest rate, it's possible to set aside a smaller sum to meet a future savings goal, and vice versa.) The discount rate on pension funds' liabilities, which is based on the yield from investment-grade corporate bonds, rose in 2013 to 4.69% from 3.93% in 2012.

The impact on interest rates is apparent from the experience of the two preceding years. According to S&P, despite 2012's 13.4% equity return, pension underfunding among the S&P 500 companies actually increased over 27%, to an aggregate $451.7 billion from $354.7 billion, owing to the decline in interest rate and the resulting increase in the present value of future liabilities. And while the 29.6% gain in the S&P 500 index in 2013 helped reduce underfunding by over 50%, to $224.5 billion, the increase in the discount rate on future liabilities "assisted considerably," S&P observed.

While 2014 is only a bit more than half over, the trends are less positive than last year's. The S&P 500 is up 7.5%, setting another record Wednesday. But contrary to expectations of virtually every forecaster, bond yields have fallen markedly this year, to 2.47% on the Treasury 10-year note as of Wednesday, a hair above the 2014 low of 2.44%.

The gain in the S&P 500 and the fall in bond yields suggest a rerun of 2012's experience, when pension fund underfunding increased despite positive equity and debt market returns.

To be sure, writes Citi's Levkovich, "the stock market is crucial to the asset side of pension story." But given the likelihood of "modest single-digit gains through mid-2015, it will not close the gap entirely."

"The most significant impact on pensions will come when interest rates move higher, thus reducing the present value of future pension obligations, which will accelerate the time line of fully funded status," he concludes.

S&P agrees, but it also avers while higher interest rates would drastically improve the funding of corporate pensions, they would also be potentially damaging to parts of the economy.

Indeed, it is difficult to reconcile pension plans' hope for higher stocks and higher bond yields. Low interest rates without a doubt have increased price-earnings multiples as low yields have lured investors into equities. Low interest rates also have provided an important lift to corporate profits as well by sharply reducing interest costs, while stock buybacks have boosted earnings per share for public corporations. The bottom lines of financial companies such as banks also have benefitted from the reduction in loan-loss reserves, which have flowed directly to the bottom line of the S&P 500.

Thus, Corporate America -- or at least the portion that still offers pension plans -- would like higher interest rates to reduce its future liabilities to retirees. But the impact on the economy and the stock market likely would be negative.

Another reason to heed the admonition to be careful what you wish for.